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WATER RESOURCES RESEARCH, VOL. 37, NO. 12, PAGES 3275-3283,
DECEMBER 2001
Riparian vegetation controls on braided stream dynamics Karen
Gran and Chris Paola Department of Geology and Geophysics and St.
Anthony Falls Laboratory, University of Minnesota Twin Cities,
Minneapolis, Minnesota, USA
Abstract. Riparian vegetation can significantly influence the
morphology of a river, affecting channel geometry and flow
dynamics. To examine the effects of riparian vegetation on gravel
bed braided streams, we conducted a series of physical experiments
at the St. Anthony Falls Laboratory with varying densities of bar
and bank vegetation. Water discharge, sediment discharge, and grain
size were held constant between runs. For each run, we allowed a
braided system to develop, then seeded the flume with alfalfa
(Medicago sativa), allowed the seeds to grow, and then continued
the run. We collected data on water depth, surface velocity, and
bed elevation throughout each run using image- based techniques
designed to collect data over a large spatial area with minimal
disturbance to the flow. Our results show that the influence of
vegetation on overall river patterns varied systematically with the
spatial density of plant stems. Vegetation reduced the number of
active channels and increased bank stability, leading to lower
lateral migration rates, narrower and deeper channels, and
increased channel relief. These effects increased with vegetation
density. Vegetation influenced flow dynamics, increasing the
variance of flow direction in vegetated runs and increasing scour
depths through strong downwelling where the flow collided with
relatively resistant banks. This oblique bank collision also
provides a new mechanism for producing secondary flows. We found it
to be more important than the classical curvature-driven mechanism
in vegetated runs.
1. Introduction
The riparian corridor encompasses a river system and its
immediate banks, an environment where the hydrosphere, the
biosphere, and the lithosphere come together. Riparian vege- tation
can substantially influence physical properties of the river,
primarily by changing bank strength and flow resistance. Numerous
studies have linked properties of river channels, including width,
depth, and velocity to vegetation density in the riparian zone
[Hadley, 1961; Brice, 1964; Zimmerman et al., 1967; Charlton et
al., 1978; Graf, 1978; Andrews, 1984; Hey and Thorne, 1986; Huang
and Nanson, 1997; Rowntree and Dollar, 1999]. Some have even found
a correlation between the type or density of vegetation and the
overall behavior of the river, changing between meandering and
braiding as the vegetation changes [Mackin, 1956; Brice, 1964;
Nevins, 1969; Goodwin, 1996]. Because of the complexity of natural
vegetated streams, however, it is often difficult to establish a
direct causal rela- tionship between vegetation density and channel
characteris- tics. Changes in vegetation density may result from
shifts in climate, water discharge, or sediment discharge, and any
of these other factors can alter channel characteristics.
We examined the relationship between riparian vegetation and
braided systems through a series of physical experiments conducted
at the St. Anthony Falls Laboratory (University of Minnesota,
Minneapolis) [Gran, 2000]. Braided rivers repre- sent the main mode
of instability for unconstrained flow over a noncohesive bed
[Murray and Paola, 1994]. They are charac-
Now at Department of Earth and Space Sciences, University of
Washington, Seattle, Washington, USA.
Copyright 2001 by the American Geophysical Union. Paper number
2000WR000203. 0043-1397/01/2000WR000203 $ 09.00
terized by multiple channels with high lateral migration rates
relative to single-thread channels. Vegetation directly opposes
this tendency to migrate freely by strengthening and stabilizing
banks. Our experiments compared braided rivers with and without
riparian vegetation to determine how vegetation af- fects channel
form and flow dynamics. Vegetation density was the main variable
between runs, and other factors that could influence the channel
form and pattern, including water and sediment discharge, grain
size, and slope, were held constant. We carried out five runs: two
with no vegetation and three with vegetation on the bars and banks.
These experiments were intended to model processes in nature,
complementing existing studies of natural streams, and provide some
additional insight into how riparian vegetation may affect braided
channel form and flow characteristics. The experiments show that
vegetation by itself can cause major changes in channel form and
flow dynamics in a braided system. The trends in channel form and
geometry compare well with trends seen in natural rivers.
2. Methods
We conducted our experiments at the St. Anthony Falls Laboratory
in a 2 m by 9 m flume (Figure 1). Water entered from a constant
head tank through a pipe directed toward the back wall of an
entrance chamber to damp turbulence. Well- rounded, well-sorted dry
quartz sand (Dso = 0.5 mm) was fed in at a constant rate with a
mechanical sediment feeder. The
bed was set to a slope of 0.014, and a straight channel was
carved down the middle of the flume 2 cm deep and 30 cm wide to
channel initial flow. We used the same water and sediment
discharge (Qw = 3.5 x 10 -4 m3/s and Qs = 1.2 g/s) for all runs,
with Qw and Qs chosen to maintain the initial slope. The initial
straight channel rapidly widened and developed into a braided
channel system. We let the flume run until most of the surface of
the study reach had been reworked by the flow
3275
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3276 GRAN AND PAOLA: RIPARIAN VEGETATION CONTROLS
:Sediment ............ 1 :':: Head Tank .-" Feeder ::[:.
:.'"'.....::: :.. 'J... :.. ".- ........ . ..... :
.......
. ., ...... . ............... :::.:......:::...:..:%?-::
.......... . .......... _. ........... .....
. ..;.' .: .:.:.:. ... .. .... .
Entrance ..... :...., Roughness Chamber Elements ;:..::..
Initial Channel
Figure 1. The upper end of the flume prior to the start of a
run. The bed surface is planed to a slope of 0.014, and a straight
channel is carved into the sand to initially channel flow. During
the run, water and sediment enter from a constant head tank and
sediment feeder into the entrance chamber. Roughness elements keep
the flow from sticking to the walls of the flume. The dye tank
holds a measured 2 ppm solution of rhodamine dye for use in depth
measurements.
before adding vegetation. To prevent the flow from migrating to
the flume walls and sticking there, roughness elements were placed
along the sides of the flume.
Care was taken to ensure that Froude numbers in the model
were comparable with those in natural systems and that flow in
the model was turbulent. Froude numbers in the model runs
ranged from 0.42 to 0.98 with an average of 0.77, indicating
subcritical flow. For comparison, Froude numbers measured on the
Sunwapta River, a gravel bed braided stream in Alberta, Canada,
ranged from 0.41 to 1.08 [Ashmore, 1988]. Reynolds numbers in the
model ranged from 800 to 3800 with an average of 1400, indicating
turbulent flow.
After the braided channel was fully established, we intro- duced
the vegetation, for which we used alfalfa (Medicago satira). Seeds
were soaked for 48-72 hours, then air dried for 6-12 hours prior to
seed dispersal. During dispersal the water discharge was halved. At
this discharge, sediment transport was minimal, so the sediment
feeder was turned completely off. The seeds were dispersed over the
flume by hand as uni- formly as possible. Some seeds landed
directly on bars or banks, and some were carried by the flow and
later deposited along banks or washed out of the flume. This method
of seed dispersal is similar to many riparian species including
willows (Salix) and cottonwoods (Populus), which disperse seeds by
both wind and water [Johnson, 1994]. While the sprouts were
growing, we maintained just enough discharge to keep the sediment
damp through groundwater flow, but it was not high enough to
actually flow through the channels. After the alfalfa
sprouts had grown for 10-14 days, each sprout had a single stem
---30 mm high and 1 mm in diameter with two to four small leaves at
the top. Roots reached a similar distance below the surface (30 mm)
and consisted of one main taproot with smaller branching rootlets.
Water and sediment discharges were returned to their original
values, and the run continued for an additional 30-36 hours of run
time. There did not
appear to be any systematic changes in flow parameters as time
progressed at the end of the run, so we do not believe the small
differences in run time affected the results.
We conducted five runs. Runs 1 and 2 had no vegetation and were
used as controls. Runs 3, 4, and 5 had mean plant den- sities of
1.2, 4.2, and 9.2 stems/cm 2, respectively (Table 1). Plant
densities were measured using average point counts of the number of
seeds in randomly selected plots on banks and bars following seed
dispersal. Since not all of the seeds germi- nated, the measured
plant densities may be slightly higher than the actual stem
densities.
For each run, we measured water depths, surface velocities, and
bed topography along five cross sections spaced 0.5 m apart in the
central portion of the flume. Water depths were measured every 2
hours using a new noninvasive image-based dye density technique.
The principle behind the technique is similar to one developed by
Winterbottom and Gilvear [1997] using airborne multispectral
imagery in natural rivers. We ran a 2 ppm (parts per million)
solution of rhodamine dye through the flume and obtained vertical
images with a digital camera. As the depth increased, the dye
appeared darker in the image.
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GRAN AND PAOLA: RIPARIAN VEGETATION CONTROLS 3277
Table 1. Summary of Channel Geometry Characteristics for Each
Run a Stem Density, Braiding Intensity Aspect Ratio Maximum Channel
Relief Topographic Correlation
Run stems/cm 2 (BI) b a c Depth, mm yd Coefficient ro e 1 0 ND f
125 _+ 43 18 + 6 0.20 + 0.06 ND f 2 0 5.0 +_ 0.3 158 +_ 57 15 +_ 4
0.14 + 0.04 0.57 3 1.2 4.1 _+ 0.3 71 +_ 22 16 + 4 0.23 + 0.08 0.75
4 4.2 3.3 +_ 0.3 101 +_ 51 19 + 5 0.27 + 0.11 0.69 5 9.2 2.4 + 0.4
21 +_ 20 25 _+ 7 0.39 _+ 0.14 0.80
aNote that these are mean values for each run. The listed
variance is one standard deviation from the mean for the entire
run. bAyerage number of active channels along a cross-section.
CActive channel width divided by the mean channel depth. dAverage
transverse slope along a cross-section. eMeasure of the degree of
correlation between consecutive bed profiles. An ro = 1 means
perfect correlation (low lateral mobility rates).
Lower r o values imply higher amounts of lateral migration. fNo
data.
We extracted the green band from the RGB images and used the
color value (0-255) in the green band as a measure of dye
intensity. We calibrated the dye method by including a calibra-
tion tray in the images. The calibration tray was a rectangular
pan, 200 mm long, coated with the same uniformly light- colored
sand used in the experiment and tilted so as to produce a linear
depth variation from 0 to 50 mm. At these depths under our
experimental conditions, dye intensity varied lin- early with depth
(Figure 2). We checked the dye-estimated depths using spot point
gage measurements throughout the runs. We eliminated any cross
sections where the point gage measurements disagreed with the
dye-based depth by >3 mm. Of the 295 cross sections measured, 47
(16%) were removed. For the 248 remaining cross sections the dye
method calcula- tions agreed with the point gage measurements with
a mean deviation of +_ 1.0 mm.
Surface velocity data were collected immediately preceding depth
measurements, so the two data sets could be correlated. We measured
surface velocities using a surface particle track- ing technique.
Liquid soap was added tO the flow upstream from the study area,
creating small bubbles. A video camera mounted directly overhead
recorded the bubbles as they floated downstream, and a particle
tracking program calcu- lated surface velocity vectors along the
paths where the bub- bles traveled. To compare the velocity data
between runs, we spatially thinned the data to remove sampling bias
favoring swiftly flowing zones. We established a grid such that at
least one data point remained in each grid cell, and the data were
then thinned randomly within each cell until only one point
remained. Statistics on the velocity vector magnitude and di-
45
y=-0.28x + 53
0
0 Light Intensity 200 Figure 2. Example calibration curve
showing the linear rela- tionship between depth and dye intensity
for depths 2 mm for our ex- perimental conditions). The BI
decreased from an average of 5.0 in run 2 to 2.4 in run 5 (Table 1
and Figure 3). In the highest density run, channel closure led to
the development of a wandering river with one or two main channels
separated by large vegetated islands (Figure 4). In plan view it
resembled a stretch of the Athabasca River upstream of Fort
Assiniboine (Figure 5), a wandering gravel bed river with two to
three main channels separated by forested islands [Neill,
1973].
Channel cross-sectional geometry changed as vegetation density
increased. Aspect ratios a were an order of magnitude lower in the
highest density run than in the unvegetated runs (Table 1 and
Figure 3). Here a = b/h, where b is the sum of all active channel
widths along a cross section and h is the mean depth. Maximum
depths h max and mean transverse slope magnitude Sy .along each
cross section increased with vegeta- tion density (Table 1 and
Figure 3). To measure Sy, we calcu- lated slope magnitudes beiween
adjacent cross-stream points on the bed and averaged across each
cross section. Sy in- creased by a factor of 2 from the unvegetated
runs to the highest density run.
Vegetation also influenced channel mobility. As an indirect
measure of channel mobility, we compared the amount of change
between bed profiles measured every 5 to 7 hours by treating the
profiles as a form of time series data and comput- ing correlation
coefficients ro between sequential profiles. This method is similar
to the method used to calculate autocorre-
lation coefficients in a single time series with a given lag
time [Bras and Rodriguez-Iturbe , 1993]:
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3278 GRAN AND PAOLA: RIPARIAN VEGETATION CONTROLS
Braidinq Intensity 7
-
o
250.. Aspect Ratio 4 Maximum Depth
0.6 Local Transverse Slopes
o
o Bed Topography Correlation Coefficients (ro) 1
0.4 0 5 10
Stem Density (#stems/cm )
Figure 3. Channel geometry characteristics for all five runs
plotted against vegetation density. Braiding intensity (BI) mea-
sures the average number of active channels along a cross section.
Aspect ratio is the average_active channel width di- vided by the
mean depth (a = b/h). The maximum depth h m refers to the maximum
depth_measured along each cross section. The local transverse slope
Sy is calculated by averaging transverse slope magnitudes between
adjacent points along a cross section. The correlation coefficient
r o is a measure of the correlation between bed topography profiles
through time. A high ro means a high degree of correlation,
indicating low channel mobility. Each data point on the graph
represents the average of all cross-sectional data for the duration
of a run. The spread represents one standard deviation up and down
from the mean for the run. Actual values can be found in Table 1.
Overall trends show a decrease in braiding intensity and aspect
ratio and an increase in maximum depth, relief, and bed stability
with increasing density of vegetation.
cov (*h, '12) ro = x/va r (r/,)var ('12) (1)
elevation at time 2, cov (rh, '12) is the covariance between r h
and '12, and var (rh) and var ('12) are the variances of r h and
'12. A perfect correlation would give an ro = 1, with lower ro
implying a lower degree of correlation between runs. Run 2 had the
lowest r o, and run 5 had the highest, indicating a higher degree
of channel stability in the densely vegetated run (Table 1 and
Figure 3). 3.2. Surface Flow Dynamics
Riparian vegetation affected flow dynamics in the experi- ments.
Velocity vector magnitudes were less variable in runs 4 and 5 than
in runs 1-3 as shown by a decrease in the coefficient of variation
c v with increasing vegetation density (Table 2). Sampling bias may
account for some excess low-magnitude data in the unvegetated runs
because the particle-tracking method does not work in slow flowing
plant-choked areas. However, even with the low-magnitude velocities
removed, the higher c v values for the unvegetated runs remain.
Interestingly, we observed no correlation between vegetation
density and mean velocity magnitude. Evidently, the cutoff of low-
discharge channels by plants and the increase in bank strength
reduce velocity variability but do not speed the flow up
overall.
The vegetated runs had a greater spread in velocity vector
angles as shown by an increase in the standard deviation of the
vector direction data o'd, indicating more sinuous flow paths in
the vegetated runs (Table 2)..Analyzing the vector angle spread
using the method detailed by Curray [1956] shows that the percent
correlation between vector angles L is lower in vegetated runs
(Table 2). We did not find a systematic decrease in L with
vegetation density. Once the vegetation is estab- lished, changes
in its density do not seem to lead to increased sinuosity of flow
paths.
3.3. Scour Features
Scour holes are ubiquitous features of braided streams, forming
wherever flow paths collide [Mosley, 1976; Ashmore and Parker,
1983; Best, 1986, 1987; Best and Ashworth, 1997; Rhoads and
Kenworthy, 1998]. In the unvegetated runs, scour holes up to five
times the mean flow depth formed throughout the stream, migrating
and filling in rapidly. Once vegetation was introduced, scour
features became much less mobile and transient, and some deepened
to as much as 6.4 times the mean flow depth. Many scour features in
the vegetated runs migrated until they encountered a vegetated bank
where they stayed fixed, sometimes for the remainder of the run.
Differ- ences in scour hole mobility can be seen in the time series
of bed elevations from cross sections that crossed major scour
features, all of which are given by Gran [2000]. For the highest
vegetation density (run 5), many of the along-bank scour fea- tures
elongated parallel to the bank and deepened.
4. Discussion
n
cov (r/,, r/2) = ] (r/,,- ,)(r/2,- 2) (2) i=1
var (rt) = n - 1 (Ti -- )2, (3) i=1
where rh and '12 represent bed topography at sequential time
steps, h is the average elevation at time 1, t2 is the average
4.1. Scaling As vegetation density in the model increased, it
affected
channel form and dynamics. Many of the observed changes in
channel geometry are consistent with an increase in bank strength
due to the introduction of vegetation and are compa- rable to
trends in natural river channels. As mentioned above, we took care
to use Froude numbers comparable to natural braided rivers and
maintain turbulent flow in model channels, so the flow dynamics can
be compared with natural rivers. The
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GRAN AND PAOLA: RIPARIAN VEGETATION CONTROLS 3279
f.- ."'
. '":
:.-. ' ,,':5... .,...- .;. .. ,:..;: ...... ;:. '';. -... :...
:.. -:..'-.-':: ,; ;...'."".' .... ;,: ......... ;:......:.;
:5' ,,' - ..**-,.... '." '"'*:..',. "'::'"F. . '" -
.%.,.:.,.%
-.:.. :
Figure 4. Image of run 5, the run with the highest spatial
vegetation density. The river resembles a wandering stream, with
one to two main channels separated by large, vegetated islands.
size of the alfalfa sprouts can be compared with natural vege-
tation as follows.
To compare length scales, we use as a prototype an unveg- etated
reach of the Sunwapta River, 1-2 km downstream from the Athabasca
glacier (Figure 6). The model used quartz sand with a Dso = 0.5 mm,
while the Sunwapta had a Dso = 40 mm. The length scale ratio
(model/prototype) is thus 0.0125. Comparisons between mean channel
width and depth gave similar scale ratios (0.008 and 0.01,
respectively), but these are values set by the flow itself and are
not independent variables.
In shape the alfalfa sprouts we used in the experiments are most
similar to trees, with a solitary trunk and high branches. Using
the length scale ratio computed above (0.0125), the 1
mm alfalfa stems scale up to 80 mm diameter field vegetation.
This is a reasonable size for young tree trunks. In addition, slow
flow through the vegetation in the model was nearly laminar as
opposed to turbulent in flow through natural bank vegetation, so
the zone of interference from each stem in the experiments is
larger than a similar zone of interference in a fully turbulent
flow. This makes the stems appear larger than they really are to
the experimental flow.
4.2. Channel Geometry Charlton et al. [1978], Andrews [1984],
and Hey and Thorne
[1986] have shown that when bank sediment type is held con-
stant, the average total wetted width/average depth (a) de-
Figure 5. A stretch of the Athabasca River near Fort Assiniboine
in Alberta, Canada, described as a wandering river by Neill [1973].
There are one to two main channels separated by large vegetated
islands. Image modified from 1:50000 map [Department of Mines and
Technical Surveys, 1959].
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3280 GRAN AND PAOLA: RIPARIAN VEGETATION CONTROLS
Table 2. Summary of Spatial Velocity Characteristics for Each
Run a
Run
Stem Mean Vector c v b Vector o'd Vector Density, Magnitude, C v
b Vector Magnitudes Angles, c
stems/cm 2 m/s Magnitudes >0.05 m/s rad
L Vector
Angles, d %
1 0 0.21 0.53 0.48 0.34 96 2 0 0.18 0.45 0.45 0.43 93 3 1.2 0.21
0.42 0.41 0.60 85 4 4.2 0.20 0.33 0.32 0.50 90 5 9.2 0.19 0.37 0.36
0.61 85
aNote that all listed values are statistical compilations from
the entire run. bHere C v is the coefficient of variation (standard
deviation/mean) of the vector magnitude data. CHere tr d is the
standard deviation of the vector angle data. dL is the percent
correlation of vector angles.
creases as the density of vegetation increases. This same trend
is seen in the experimental runs, with high vegetation density
corresponding to lower a. In the unvegetated model runs, a was an
order of magnitude higher than in run 5 and the natural
single-thread rivers. High a are characteristic of braided rivers
[Ashmore, 1985], and a computed in runs 1 and 2 are consistent with
a computed for other braided streams [Eschner, 1983]. Run 5, with
the highest vegetation density, had an average a - 21, which is
within range of a computed from natural single- thread channels
[Charlton et al., 1978; Andrews, 1984; Hey and
& N
o 2 km
Glacier snout Alluvial fan Rock gorge Braid plain
%
\ \ Study , ........ each
Mount Kirchner 3511 Gauging Station/
Athabasca_ Glacier ,,,/--'%
Figure 6. This map shows the location of the prototype sec- tion
of the Sunwapta River in Jasper National Park, Alberta, Canada.
Thorne, 1986]. The braiding index was also lowest in this run,
and in plan view the channel resembled a wandering river (Figures 4
and 5). Although it was clearly not a meandering river, it was
shifting toward a meandering behavior rather than strictly
braiding. It has proven quite difficult to model true meanders in a
flume [Smith, 1998], and one of the main rea- sons may be lack of
vegetation [Hickin, 1984].
The observed decrease in a with increasing vegetation is the
result of several factors. One of these is the closure of small
channels by vegetation, forcing the bulk of the discharge into
fewer channels. This showed up as a decrease in braiding intensity
with increasing density of vegetation. This decrease in the number
of active channels led to a decrease in the total
channel width partially accounting for the observed decrease in
a. The decrease in a also results in part from an increase in bank
strength as more plants and thus more roots became established on
the banks. Although root density was not mea- sured directly, root
density scales with stem density. Roots add tensile strength to the
sediment, increasing the bulk shear strength [Vidal, 1969; Thorne,
1990], and the strength increases with increasing density of roots
[Ziemer, 1981; Gray and Mac- Donald, 1989]. In addition, the
roughness introduced by bank vegetation increases the local
boundary layer thickness, forcing the high-velocity zone away from
the bank and decreasing shear stress on the bank [Thorne and
Furbish, 1995]. As bank strength increases, deeper, narrower
channels can develop. Brice [1964] found that the Calamus River in
the Nebraska Sandhills had a straight, narrow channel where
erosional re- sistance was high and wide, braided channels where
bank ero- sional resistance was low. The main factor controlling
ero- sional resistance of the banks was vegetation.
An increase in bank strength also increases channel relief
through the formation of higher or steeper banks. Channel relief
increased with vegetation density in our experiments, consistent
with an increase in bank strength. An increase in bank strength
should also affect lateral migration rates; in the experiments,
this is expressed as a decrease in channel mobility with increasing
vegetation density. This decrease in erodibility and lateral
mobility resulting from vegetated banks and bars has been
quantified in the field on anastomosing [Smith, 1976] and
meandering streams [Beeson and Doyle, 1995]. 4.3. Scour
Features
The increased depth of scour features, particularly near- bank
scour features, is consistent with an increase in bank strength due
to the presence of vegetation. In an unvegetated braided system,
flow impinging on the bank tends to erode the bank, widening the
channel. When the banks become stabi-
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GRAN AND PAOLA: RIPARIAN VEGETATION CONTROLS 3281
b
Top view
sur V / $
Cross-sectional View
Figure 7. Definition sketch for the vortex generated due to bank
impingement. The sketch on the left shows the angle of attack O
between the flow line and the bank. The sketch on the right shows a
cross-sectional view through the flow. The vortex generated by bank
impingement is assumed to encompass the entire flow depth h. Here r
is radius of vortex, t/surf is down- stream surface velocity
component, p is density of water, and % is basal shear stress.
Figure 8. Definition sketch for secondary flow generated from
channel curvature. The formulation is in curvilinear co- ordinates.
R is radius of curvature, u is the downstream veloc- ity component,
and v is the cross-stream velocity component.
lized with vegetation, flow impinging on the bank cannot erode
the bank as readily, and flow may be directed downward, scour- ing
the bed. This process is similar to the classic horseshoe vortex
formed when flow impinges upon a vertical cylinder, scouring the
bed around the cylinder [Shen and Schneider, 1969].
In order to determine how strong the helical flow generated by
oblique bank impingement might be we developed a simple model of an
impingement-driven vortex. The shear stress gen- erated from
secondary flow due to oblique bank impingement is then compared to
the shear stress generated by curvature- driven secondary flow to
determine the relative importance of the bank impingement
vortex.
The shear stress generated by flow impinging on the banks can be
described with a simple torque balance (Figure 7). If we assume
that a vortex with a horizontal rotation axis generated by the
downwelling develops through the entire flow depth, a torque
balance can be written with the lever arm equal to half the flow
depth. The driving force is the pressure imbalance at the wall.
Using the angle of attack O between the flow and the bank, we
extract from the near-bank velocity the vector com- ponent
perpendicular to the wall, which drives the vortex. The torque is
given by torque/area = pressure x lever arm:
A -- P(Usurf sin 0) 2 h (4) - , where p is density of water,
t/surf is surface velocity in down- stream direction, and h is flow
depth. This torque is balanced by shear stress % along the bed and
the wall and rewritten with shear stress on the left-hand side:
2 sin 20 Tb t/surf p 8 '
This form of % is compared with the basal shear stress gen-
erated by secondary flow due to curvature Zc (Figure 8) [e.g.,
Roszovskii, 1957; Smith and McLean, 1984]. Note that our goal here
is an estimate of the magnitude of the stress due to secondary
flow, not a detailed model of the secondary flow field. To first
order, secondary flow in a wide curved open channel under steady
conditions and without streamwise to-
pography is described by a basic force balance in curvilinear
coordinates:
u(z) 2 10P 10zy = (6) R pOy pOz'
where u(z) is the downstream velocity component, R is radius of
curvature, P is pressure, and Zy is shear stress. The trans- verse
pressure gradient is balanced by centrifugal acceleration at the
point of mean velocity 5. Integrating over depth, we get an
equation in terms of bed shear stress Zc:
h t/(Z)2 __ 2 Tc R dz = --, p o (7) where Zo is the standard
roughness length. We then introduce a shape factor/3 such that/3
-< 1'
h [t/(Z) 2-- 2] dz 0 /3 = h52 . (8)
Combining (7) and (8), we have an equation for the shear stress
generated by secondary flow due to curvature:
q'c 2h p R ' (9)
Now the shear stresses from (5) and (9) can be compared to get
an estimate of the relative importance of the bank impinge-
ment-generated shear stress:
- -'-- Rsin 20 ' Tb t/surf
From this ratio, it becomes clear that the main variables of
interest are flow depth h, radius of curvature R, and angle of
impingement O.
Twenty-five scour holes from runs 4 and 5 were examined in the
vegetated runs to determine ratios of Zc/%. For these 25 scour
holes the average bank impingement angle is 39 , the mean radius of
curvature is 0.34 m, and the average pool depth
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3282 GRAN AND PAOLA: RIPARIAN VEGETATION CONTROLS
is 0.021 m [Gran, 2000]. In all but one of the scour holes the
shear stress related to a bank impingement-generated vortex is
greater than the shear stress related to curvature-driven secondary
flow. Shear stress ratios (equation (10)) ranged from 0.004 to
3.18, with a median of 0.10. This indicates that bank impingement
vortices are an important source of secondary flow in vegetated
braided streams and suggests that it would be worth developing a
detailed model for vortex generation at resistant banks and the
subsequent evolution of the vortex as it interacts with the flow
field.
4.4. Surface Flow Dynamics Other evidence that vegetation
affected flow dynamics was
seen in comparisons of velocity vector statistics between runs.
We measured an increase in velocity vector angle deviation with the
addition of vegetation. This angle deviation increase is probably
related to flow moving around vegetated bars and islands of higher
resistance. As flow moves downstream toward a vegetated island, it
can either flow across the island, a shorter path with higher
resistance, or around the island, a longer path with lower
resistance. Because the length of the flow path around the island
varies depending on the width of the bar or island and the
resistance varies with the density of vegetation, the proportion of
flow moving around the island depends in part on both the geometry
of the island and the density of vegetation.
To test the possibility that the increased angle deviations are
the result of flow steering around zones of higher resistance, we
linearized a two-dimensional flow model and introduced a
small-scale sinusoidal perturbation to the flow resistance in
two dimensions [Nayfeh, 1993]. This had the effect of creating
islands of higher resistance, similar to the vegetated braided
systems in our flume. Using this model, we introduced a small-
scale perturbation e to the resistance CT and analyzed the
resulting velocity field. For the experiments, o- a increased 0.07-
0.27 rad between runs with and without vegetation. We used the
linearized system to see if it was possible to achieve the increase
in o'a seen in our experimental data [Gran, 2000].
We found that to get an increase in o- a of 0.07 rad, e had to
be at least 0.53; that is, the resistance had to vary by 53%. An e
= 0.53 translates into a maximum Cf = 0.13. We computed an estimate
of Cf for our experimental vegetation by approx- imating the stems
as vertical cylinders and summing the drag along each cylinder set
into the flow plus the bed resistance. For our lowest density run
this gives a CT = 0.18, which is comparable to but still higher
than the maximum CT in the linear perturbation model using e =
0.53. That the linearized theory does not work perfectly is not
surprising; an e = 0.53 is hardly a small perturbation, so rather
it is surprising that the linearized theory comes as close as it
does. It should be more applicable at lower vegetation densities.
Observationally, there also appears to be a threshold density where
the resistance is so high that flow is essentially blocked by the
vegetation, and the bulk of the flow is forced around the
vegetation. Our vegeta- tion densities were all above this
threshold. This could explain why we saw no link between o'a and
increasing vegetation densities.
If vegetated islands tend to block the flow completely, then
island geometry should control variability in flow direction.
Island geometry was primarily a function of the geometry of exposed
bars when the flume was seeded rather than vegeta- tion density.
Differential erosion at the edges of islands was minor compared
with the initial location of bars prior to seed-
ing. To see if island geometry alone could account for the
increase in the flow angles, we measured the length and width of 12
islands from runs 4 and 5 and computed an average length to width
ratio of 2.2. The inverse tangent of this ratio gives a
characteristic angle of flow deviation equal to 0.4 rad. If we
assume that the flow affected by the islands has a typical
deviation angle of 0.4 rad, then only 2.4-26% of the total flow
must be influenced by islands to cause a flow deviation increase of
0.07-0.27 rad. Although this is a simple analysis, it strongly
suggests that the flow deviation is a direct result of island
geometry. Since island geometry is not primarily a function of
vegetation density, it is again not surprising that we observed no
trends in angle deviation between the three vegetated ex-
perimental runs.
5. Conclusions
Our study was designed to test if vegetation alone could affect
channel geometry and flow dynamics in a braided system and to
determine how the magnitude of the effects varies with vegetation
density. By running a series of physical experiments where the only
variable was vegetation density and other vari- ables, including
grain size, slope, sediment discharge, and wa- ter discharge, were
held constant, we were able to show that riparian vegetation can
substantially alter channel geometry and flow characteristics. Our
results indicate that as vegetation density increases, lateral
mobility decreases, braiding intensity decreases, width to depth
ratios decrease, maximum channel depths increase, and channel
relief increases. The relationships we observed between vegetation
density and channel geome- try, bank stability, and lateral
mobility are similar to many observed in natural rivers, even
though most field studies ex- amining variable vegetation density
effects have concentrated on single-thread channels. Of particular
relevance to braided systems is the relationship between scour
holes and vegetated banks and bars. This includes decreased scour
hole mobility, increased scour hole depth, and the introduction of
oblique bank impingement-driven secondary flow in channels with
riparian vegetation.
In the run with the highest vegetation density, width to depth
ratios approached those of natural single-thread channels, the
braiding intensity decreased, and in plan view the model re-
sembled a wandering river, with one to two main channels flowing
around larger vegetated islands. Although we cannot tell if changes
in vegetation alone are enough to alter the general pattern of a
river from braided to meandering, we have shown that vegetation
plays an important role in stabilizing the banks, constraining
channel migration, and allowing deeper and narrower channels to
develop. These are all effects that move the channel pattern in the
direction of meandering.
Acknowledgments. This research was funded through a grant from
the National Science Foundation (EAR-9628393). Additional funding
came from a Graduate School Fellowship through the University of
Minnesota and a Francis Gibson Fellowship through the Department of
Geology and Geophysics. We appreciate the comments from two
anonymous reviewers.
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K. Gran, Department of Earth and Space Sciences, University of
Washington, Seattle, WA 98195, USA. ([email protected])
C. Paola, Department of Geology and Geophysics and St. Anthony
Falls Laboratory, University of Minnesota, Twin Cities,
Minneapolis, MN 55455, USA.
(Received January 10, 2001; revised April 2, 2001; accepted June
23, 2001.)